To determine the degree of the polynomial [tex]\( h(x) = 6x^3 - 7x^5 + 2x^8 - 3x + 55 - 3x^4 \)[/tex], we need to find the highest power of the variable [tex]\( x \)[/tex].
Let's break down the polynomial by identifying the degrees of each term:
- The term [tex]\( 6x^3 \)[/tex] has a degree of 3.
- The term [tex]\( -7x^5 \)[/tex] has a degree of 5.
- The term [tex]\( 2x^8 \)[/tex] has a degree of 8.
- The term [tex]\( -3x \)[/tex] has a degree of 1.
- The constant term [tex]\( 55 \)[/tex] has a degree of 0 (since it can be written as [tex]\( 55x^0 \)[/tex]).
- The term [tex]\( -3x^4 \)[/tex] has a degree of 4.
Now, we compare the degrees of all the terms: 3, 5, 8, 1, 0, and 4.
The highest degree among these is 8.
Therefore, the degree of the polynomial [tex]\( h(x) \)[/tex] is [tex]\(\boxed{8}\)[/tex].
